In communication systems, data that can represent a picture, voice, etc., is transmitted through the system using a communication medium or channel. The channel can be wired or wireless. In either case, the channel characteristics, which can be represented as, e.g., a channel transfer function, often distorts the data that it transmits. In order to compensate for such distortion, receivers make channel estimates, which they then use, to try and reverse the distortion introduced by the channel.
There are several factors that introduce distortion in transmitted signals. For example, noise, inter symbol interference (ISI), etc., and in wireless systems multi-path. In wireless systems, when a transmitter transmits a signal, it may be reflected off buildings, cars, the ground, etc. before it reaches a receiver, and/or it may arrive at a receiver without being reflected at all. In cities, reflections can be particularly problematic. Since reflected signals travel longer paths, they arrive at a receiver at a slightly later time than the original signals and appear as a ghost signal. The staggered received signals, e.g., original and ghost signals, interfere with each other and the receiver receives a distorted signal. Such interference is sometimes called multi-path interference.
Orthogonal Frequency Division Multiplexing (OFDM) is a signal processing technique used to transmit data in several modern communications systems. In the case of OFDM systems tones are transmitted orthogonal to each other to thereby avoid or minimize mutual interference. In an OFDM system, each tone may be used to transmit a different unit of data, e.g., symbol, in parallel. In many situations, OFDM receivers depend on accurate estimates of the channel transfer function to reverse distortion introduced by the channel. A key feature of OFDM is the fact that channel equalization is performed not by a multi-tap filter, but by a single division across each of a plurality of spectral bins, where each bin represents channel information for a particular tone generated over one or more time periods. The division operation is performed after an estimate of the channel's transfer function, i.e., a channel estimate, is obtained.
Channel estimates in many OFDM systems are calculated by processing pilot tones sent by a transmitter. At the receiver, a known pilot tone pattern is expected. Any deviation of the received pilot tone from this expected pattern, in amplitude and/or phase, is measured and declared the channel estimate, x. Once the channel estimate has been determined, each received FFT data bin is divided by this channel estimate. Poor estimates of channel transfer functions lead to a lower recovered signal to noise ratio (SNR) signal and hence poorer (higher) bit error rates.
As is known in the art, a current problem with the known channel estimation technique is noise enhancement. Spectral bins that have experienced destructive multi-path interference have a low value channel estimate, x. The simple 1/x division operation is non-linear and tends to enhance the noise within each bin that has a low channel estimate absolute value. Unfortunately, while the signal of interest will be set to its proper level, the noise within a bin will be enhanced by the inverse of the depth of any multi-path null that may occur in a tone corresponding to a bin, possibly rendering the data bin for a particular tone useless. One method to avoid this problem is to perform a spectral filtering operation on the channel estimate.
The idea behind channel estimate filtering exploits the fact that adjacent bins will be correlated by the coherence bandwidth of the channel. OFDM systems use a guard interval to protect against multi-path. The guard interval can be, e.g., a copy of a portion of the signal. The duration of the guard interval sets what the expected coherence bandwidth of the channel will be. The goal of OFDM is to make the coherence bandwidth of the signal smaller than that of the channel. If successful, all bins remain orthogonal and data can be recovered, even in severe multi-path, with no inter-channel interference (ICI) and/or inter-symbol interference (ISI) interference.
The guard interval determines how much filtering can be performed in the frequency domain. The goal of a spectral estimate filter is to smooth the noise corrupted spectral estimate, while not distorting the multi-path estimate. To achieve this, the bandwidth of the spectral filter, when transformed into the time domain, should pass multi-path information with no distortion. That is, the bandwidth of the spectral filter should be equal to or larger than the guard interval, if viewed from the perspective of bandwidth and not time delay. In addition, the phase relationship between the in-phase and quadrature components of the multi-path should not be disturbed. The multi-path information contained in the guard interval should be passed within the filters pass-band and all other portions of the symbol duration should be rejected. Generally, in the art, a complex low pass filter is used for this task since complex filter transform characteristics have the advantage of not necessarily being symmetrical in contrast to real filters which are symmetrical.
Complex finite impulse response (FIR) filters, regardless of the number of taps used, usually require 4 multiplies and 2 adds per tap, in addition to the adder tree that sums the filter's inner product. Real filters only require 1 multiply per tap. Therefore, complex low pass filters are 4 times as complex, in terms of multiplies per tap at least, than real only filters, which may be implemented, e.g., as either fixed, or time varying via the least mean square (LMS) algorithm.
The savings in hardware computation complexity could be significant if real and not complex filters could be used for spectral filtering as part of a channel estimation and compensation process in a multi-tone communication system. Unfortunately, low pass filtering using real filters in the presence of multi-path interference, with its potentially severe nulls, tends to cause distortion in the channel estimate. Since multi-path can be a problem in OFDM systems the use of real filters as part of a channel estimation process has the potential for worsening reception capabilities where OFDM already suffers from multi-path interference.
Accordingly, there is a need for methods and apparatus for simplifying the complexity of spectral filtering in multi-path systems. It would be desirable if spectral filtering could be implemented using real low pass filters instead of complex low pass filters as part of the channel estimation process. However, in cases where real low pass filters are used, the methods and apparatus should address the problem of distortion introduced by real as opposed to complex, low pass filtering, when multi-path interference is present.